Apparently cheese grease contaminates the cardboard:
Paper is particularly susceptible to food and beverage contamination, and it "ends up suffering the most from getting mixed with other materials," says [Natural Resources Defense Council Senior Research Specialist Darby] Hoover. The culprits: gooey cheese and oil stains. Even if you remove the crusty cheese and sauce the slices leave behind, grease will have already soaked into the cardboard, ruining it for recycling. In a single-stream system (where bottles, glass, paper, and more all co-mingle) residue from other items in the bin could also contaminate the cardboard. Food and oil can't be separated from paper in the pulping process, so once paper is soiled, it's a done deal.
Well, that's unfortunate. Probably too much to hope they start putting pizza in recyclable polymer boxes.